proving that lines are parallel Theorem: Converse of the corresponding angles Postulate
if two lines are cut by a transversal in such away that corresponding angles are congruent, then the two lines are parrallel
Example:
Original statement: If two lines cut by a transversal are parallel, then corresponding angles are congruent, then the two lines are parallel.
Converse: If corresponding angles are congruent, then two lines cut by a transversal are parallel. Converse of the same-side interior angles throrem
if two lines are cut by a transversal in such a way that same-side interior angles are supplementary, then the two lines are parallel. converse of the alternate interior angles theorem
if two lies are cut buy a transversal in such a way that alternate interior angles are congruent, then the two lines are parallel. Converse of the Alternate Exterior Angles Theorem
If two lines are cut by a transversal in such a way that alternate exterior angles are congruent, then the two lines are parallel. Theorem
If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. Theorem
If two coplanar lines are parallel to the same line, then the two lines are parallel to each other. Triangle Sum Theorem
The angles of a triangle add up to 180 degrees.
Theorem: Converse of the corresponding angles Postulate
if two lines are cut by a transversal in such away that corresponding angles are congruent, then the two lines are parrallel
Example:
Original statement: If two lines cut by a transversal are parallel, then corresponding angles are congruent, then the two lines are parallel.
Converse: If corresponding angles are congruent, then two lines cut by a transversal are parallel.
Converse of the same-side interior angles throrem
if two lines are cut by a transversal in such a way that same-side interior angles are supplementary, then the two lines are parallel.
converse of the alternate interior angles theorem
if two lies are cut buy a transversal in such a way that alternate interior angles are congruent, then the two lines are parallel.
Converse of the Alternate Exterior Angles Theorem
If two lines are cut by a transversal in such a way that alternate exterior angles are congruent, then the two lines are parallel.
Theorem
If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.
Theorem
If two coplanar lines are parallel to the same line, then the two lines are parallel to each other.
Triangle Sum Theorem
The angles of a triangle add up to 180 degrees.